Week 6 Partial differential equations 1 Heat equation
... on 0 ¤ x ¤ L, t ¥ 0, with initial distribution of temperature upx, t 0q fpxq. Recalling that upx, tq is the temperature of the rod at position x and time t, discuss in your group what the following boundary conditions correspond to physically: (1) up0, tq 10, ut pL, tq 0 . ...
... on 0 ¤ x ¤ L, t ¥ 0, with initial distribution of temperature upx, t 0q fpxq. Recalling that upx, tq is the temperature of the rod at position x and time t, discuss in your group what the following boundary conditions correspond to physically: (1) up0, tq 10, ut pL, tq 0 . ...
PROYECTO FONDECYT N° 1020578
... determine the parameter gradient by formal differentiation of discretized equations and by their numerical solution. The decisive step in this method is the elimination of a gradient that is usually difficult to determine by the solution of an additional adjoint problem. Thus , the basic approach is ...
... determine the parameter gradient by formal differentiation of discretized equations and by their numerical solution. The decisive step in this method is the elimination of a gradient that is usually difficult to determine by the solution of an additional adjoint problem. Thus , the basic approach is ...
Problem of the Week Problem D and Solution More Factors to
... The first integer in each product is the smaller of the two integers and is therefore the value of x. The second integer in each pair is larger and corresponds to y + 1. So, the value of y is 1 less than the second integer in each of the products. Therefore, the ordered pairs satisfying xy + x = 391 ...
... The first integer in each product is the smaller of the two integers and is therefore the value of x. The second integer in each pair is larger and corresponds to y + 1. So, the value of y is 1 less than the second integer in each of the products. Therefore, the ordered pairs satisfying xy + x = 391 ...
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.